广义耗散马约拉纳线的拓扑态
Topological states of generalized dissipative Majorana wires
AI总结：
该研究针对广义一维耗散马约拉纳线模型，定义了卷绕数作为拓扑不变量，揭示了量子跳跃、不平衡耦合对马约拉纳束缚态及卷绕数的调控作用，且公式可扩展至多类耗散拓扑相。
AI中文摘要：
我们研究对应于马约拉纳线的广义一维量子耗散模型，该模型在每一端可拥有多个马约拉纳束缚态。系统由一维费米子开放量子系统构成，其动力学由二次林德布拉德方程描述。利用费米子两点关联的伴随林德布拉德方程，我们发现了一般一维模型的阻尼谱和纯度谱中的能隙。随后，通过基于对称性的分类，我们证明可以定义一个作为拓扑不变量的卷绕数，该卷绕数可区分存在阻尼和纯度能隙时系统的不同稳态。接着，我们聚焦于具有不同林德布拉德量子跳跃项的特定模型，通过计算阻尼、纯度能隙以及卷绕数来探究它们的相图。特别地，我们表明，通过引入次近邻格点间的量子跳跃，可以获得更高的卷绕数，等效于更多的马约拉纳束缚态；此外，通过引入不平衡耦合，我们可以在具有负卷绕数和正卷绕数的状态之间切换。最后需要说明的是，由于我们的公式基于费米子关联而非马约拉纳算符，因此它可以轻松扩展到属于其他对称性类别的耗散拓扑相。
英文摘要：
We study the generalized one-dimensional (1D) quantum dissipative models corresponding to a Majorana wire which can possess more than one Majorana bound state at each end. The system consists of a 1D fermionic open quantum system whose dynamics is governed by a quadratic Lindblad equation. Using the adjoint Lindblad equation for the fermionic two-point correlations, we find the gaps in the damping and purity spectra of a generic 1D model. Then, using the symmetry-based classification, we show that a winding number as the topological invariant can be defined which distinguishes different steady states of the system in the presence of damping and purity gaps. Then we focus on certain models with different Lindblad quantum jump terms and explore their phase diagrams by calculating the damping and the purity gaps as well as the winding number. In particular, we show that by inclusion of quantum jumps between next-nearest-neighbor sites, higher winding numbers and, equivalently, more Majorana bound states can be achieved. Also, by introducing imbalanced couplings, we can switch between states with negative and positive winding numbers. Finally, we should mention that since our formulation is based on the fermionic correlations rather than the Majorana operators, it can be easily extended to the dissipative topological phases belonging to other symmetry classes.
